Question

Find the exact value of sin(arctan(2)). For full credit, explain your reasoning.

Answer 1

Draw a right triangle to get this

Answer 2

we have arctan(2)

this means that there is some angle x such that

tan(x) = 2

remember that tangent is opposite over adjacent, so

tan(x) = 2

tan(x) = 2/1

So opposite = 2, adjacent = 1 and we can fill out the drawing to get

Answer 3

now how do we find the value of h (the length of the hypotenuse)?